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Department of Business Studies, Aarhus School of Business, University of Aarhus Finance Working Papers, Department of Business Studies, Aarhus School of Business, University of Aarhus

No 01-3:
Bootstrap Inference in Semiparametric Generalized Additive Models.

Wolfgang Härdle, Sylvie Huet, Enno Mammen () and Stefan Sperlich

Abstract: Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y , covariates X, T the model is E(Y | X; T) = G { X T β + α + m1(T1) + . . . + md(Td) }. Here, G is a known link, â, á are unknown parameters, and m1, . . . , md are unknown (smooth) functions of possibly higher dimensional covariates T1, . . . , Td. Estimates of m1, . . . , md, α and β are presented and asymptotic distribution theory for both the non-parametric and the parametric part is given. The main focus is the application of boot-strap methods. It is shown that bootstrap can be used for bias correction, hypothesis testing (e.g. component-wise analysis) and the construction of uniform confidence bands. Various bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of our methods is illustrated in simulations and in an application to East-West German migration.

43 pages, March 12, 2001

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